Find a polynomial f(x) of degree 3 with real coefficients and the following zeros?

1,3-i

1 Answer
Apr 30, 2018

#f(x)=x^3-x^2-6x^2+16x-10#

Explanation:

If #3-i# is a zero, then #3+i# must be a zero as they are conjugates:

#f(x)=(x-1)(x-(3-i))(x-(3+i))#

#f(x)=(x-1)(x^2-x(3+i)-x(3-i)+9+1)#

#f(x)=(x-1)(x^2-6x+10)#

#f(x)=x^3-x^2-6x^2+16x-10#